Finite Group Databasebeta

← C4×#14583069 #25102475

Subgroups — C4×#14583069 #25102475

Order 11008.

1578 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063370C211yesmaximal, characteristic, complemented
2C2×#14583069C211yesmaximal, characteristic
3C4×#13063353C212yesmaximal, complemented
4C4×#13063321C211yesmaximal, characteristic, complemented
5#19134991C211yesmaximal, characteristic, complemented
6#19134970C212yesmaximal, complemented
7#19134824C212yesmaximal, complemented
8#19134807C211yesmaximal, characteristic, complemented
9#19134551C211yesmaximal, characteristic, complemented
10C4×#13063251C212yesmaximal, complemented
11C4×#100×C43C211yesmaximal, characteristic, complemented
12C2×#13063370C2211yescharacteristic
13C2×#13063353C2212yes—
14C2×#13063321C2211yescharacteristic
15#14583380C2212yes—
16#14583378—22no—
17#14583374C2211yescharacteristic
18#14583372—22no—
19#14583371—22no—
20C4×#10621898C2212yes—
21C4×#10621900—22no—
22C2×C4×D172C2211yescharacteristic, complemented
23C2×C4×C22⋊D43—22no—
24C2×C4×C22⋊D43—22no—
25C4×D4×D43—22no—
26#14583069C418yesdirect product factor
27#14583012—22no—
28#14583001—22no—
29C4×#10621873—22no—
30C4×D344—22no—
31#14582941C2212yescomplemented
32C2×#13063251C2212yes—
33C2×#13063251C2212yes—
34#14582905C2212yescomplemented
35#14582901C2212yes—
36#14582802C2211yescharacteristic
37#14582800C2211yescharacteristic, complemented
38#14582799—22no—
39#14582768C2211yescharacteristic, complemented
40C42×Dic43C2211yescharacteristic, complemented
41#14582660C2212yescomplemented
42#14582660C2212yescomplemented
43C2×C4×D4×C43C2211yescharacteristic
44C2×#100×C43C2211yescharacteristic
45C2×#100×C43C2211yescharacteristic
46C4×M16×C43C2212yescomplemented
47C43×#343C2212yescomplemented
48#13063370—22no—
49#13063370—24no—
50#13063370C2×C414yescomplemented
51C2×#10621898C2312yes—
52C2×#10621900—22no—
53C22×D172C2311yescharacteristic
54C22×C22⋊D43—22no—
55C22×C22⋊D43—22no—
56C2×D4×D43—22no—
57C22×C4×D43—22no—
58C22×C4×D43—21no—
59#13063353—24no—
60#13063353C2×C418yescomplemented
61C2×#10621873—22no—
62C2×D344—22no—
63#13063321—22no—
64#13063321C2×C414yescomplemented
65C4×Dic86D412yescomplemented
66C4×Dic86D412yescomplemented
67#13063290—22no—
68C4×D172—22no—
69C4×D172—22no—
70C4×D172D412yescomplemented
71C4×D172D412yescomplemented
72D4×Dic43—22no—
73D4×Dic43—22no—
74#13063287—22no—
75C4×C22⋊D43—24no—
76C4×C22⋊D43—24no—
77C4×C22⋊D43—22no—
78C4×C22⋊D43—24no—
79C4×C22⋊D43—22no—
80C4×C22⋊D43—48no—
81(C22⋊D43)⋊C4—24no—
82(C22⋊D43)⋊C4—24no—
83#13063284C2312yes—
84#13063283—22no—
85#13063282—22no—
86#13063281—24no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4—22no—
90C4⋊C4×D43—22no—
91C2×C22⋊Dic43—22no—
92C2×C22⋊Dic43—22no—
93C2×(C2×D43)⋊C4—22no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—22no—
96C22⋊C4×D43—24no—
97C2×C4×Dic43—22no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102C42×D43—22no—
103#13063259—22no—
104#13063257—22no—
105#13063251—24no—
106#13063251C2×C418yescomplemented
107#13063250—22no—
108#13063247—22no—
109#13063247—22no—
110#13063247—22no—
111C22×D4×C43C2311yescharacteristic
112C23×C4×C43D412yes—
113C2×M16×C43C2312yes—
114C2×M16×C43C2312yes—
115C4×D4×C43—22no—
116C4×D4×C43—22no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43D412yes—
119C2×C42×C43C2311yescharacteristic
120#100×C43—22no—
121#100×C43C2×C414yescomplemented
122#97×C43—22no—
123C4×C8×C43—22no—
124C24×C43C2×D412yes—
125C23×D43—22no—
126C23×D43—21no—
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43C22×C412yes—
130C2×D4×C43#4112yes—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—44no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—24no—
139C2×C22⋊D43—28no—
140C2×C22⋊D43—28no—
141C2×C22⋊D43—28no—
142C2×C22⋊D43—22no—
143C2×C22⋊D43—44no—
144C2×C22⋊D43—44no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151#10621900—28no—
152#10621900—28no—
153D4×D43—28no—
154D4×D43—28no—
155#10621898—22no—
156#10621898—22no—
157#10621898C22×C414yes—
158#10621898#4114yes—
159C2×D172—21no—
160C2×D172—22no—
161C2×D172—22no—
162C2×D172C22×C412yescomplemented
163C2×D172C2×D412yes—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—24no—
167C2×C4×D43—22no—
168C2×C4×D43—44no—
169C2×C4×D43—41no—
170C2×C4×D43—41no—
171C2×C4×D43—84no—
172C2×Dic86C2×D412yes—
173M16×C43—22no—
174M16×C43—22no—
175M16×C43—22no—
176M16×C43C22×C414yescomplemented
177C2×C8×C43—22no—
178C2×C8×C43—22no—
179C4⋊C4×C43—22no—
180C22⋊C4×C43—24no—
181C42×C43C2×D412yes—
182C42×C43C2×D412yes—
183C22⋊Dic43—24no—
184C22⋊Dic43—22no—
185C22⋊Dic43—44no—
186(C2×D43)⋊C4—24no—
187(C2×D43)⋊C4—22no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—44no—
190(C2×D43)⋊C4—42no—
191C4⋊Dic43—22no—
192C4⋊Dic43C2×D412yes—
193C4⋊Dic43C2×D412yes—
194Dic43⋊C4—24no—
195Dic43⋊C4—22no—
196Dic43⋊C4—22no—
197Dic43⋊C4—44no—
198C4×Dic43—24no—
199C4×Dic43—24no—
200C4×Dic43—22no—
201C4×Dic43—22no—
202C4×Dic43—22no—
203C4×Dic43—21no—
204C4×Dic43—22no—
205C4×Dic43—42no—
206C4×Dic43C22×C412yescomplemented
207D344—28no—
208#10621873—28no—
209C23×C43—22no—
210C23×C43—22no—
211C23×C43—42no—
212C23×C43—42no—
213C23×C43C4×D414yes—
214C23×C43C22×D411yescharacteristic
215C22×D43—22no—
216C22×D43—28no—
217C22×D43—22no—
218C22×D43—42no—
219C22×D43—42no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—82no—
223C22×D43—82no—
224D4×C43—24no—
225D4×C43—24no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—41no—
229C2×C4×C43—44no—
230C2×C4×C43—42no—
231C2×C4×C43—82no—
232C2×C4×C43#12012yes—
233C2×C4×C43#12011yescharacteristic
234C2×C4×C43#12011yescharacteristic
235C2×C4×C43C23×C411yescharacteristic
236C2×C4×C43C22×D412yes—
237C2×C4×C43C2×#4112yes—
238C2×C4×C43C2×#4111yescharacteristic
239C22⋊D43—216no—
240C22⋊D43—24no—
241C22⋊D43—24no—
242C22⋊D43—416no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—28no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—42no—
254C2×Dic43—41no—
255C2×Dic43—82no—
256C2×Dic43—82no—
257D172—24no—
258D172—22no—
259D172—42no—
260D172C4×D414yescomplemented
261C4×D43—24no—
262C4×D43—24no—
263C4×D43—44no—
264C4×D43—82no—
265C4×D43—84no—
266C4×D43—82no—
267C4×D43—82no—
268Dic86—22no—
269Dic86C4×D414yescomplemented
270C8×C43—24no—
271C8×C43—42no—
272C4×#453—431nomaximal, Sylow
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—24no—
276C22×C43—44no—
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—82no—
280C22×C43C2×C4×D411yescharacteristic
281C22×C43C2×#12011yescharacteristic
282C22×C43#52511yescharacteristic
283C2×D43—24no—
284C2×D43—42no—
285C2×D43—42no—
286C2×D43—44no—
287C2×D43—42no—
288C2×D43—88no—
289C2×D43—82no—
290C2×D43—81no—
291C2×D43—81no—
292C4×C43—21no—
293C4×C43—22no—
294C4×C43—42no—
295C4×C43#45312yescomplemented
296C4×C43C2×C4×D412yes—
297C4×C43#52512yes—
298Dic43—24no—
299Dic43—24no—
300Dic43—42no—
301Dic43—42no—
302Dic43—42no—
303Dic43—81no—
304C4×H(5,𝔽2)—431no—
305C2×#453—431no—
306C4×AGL(1,ℤ/8)—432no—
307C4×#127—431no—
308#1887—431no—
309#1883—432no—
310#1859—432no—
311#1856—431no—
312#1792—431no—
313C4×#104—432no—
314C4×#100D4311yescharacteristic, complemented
315C2×C43—21no—
316C2×C43—21no—
317C2×C43—44no—
318C2×C43C4×#12011yescharacteristic
319C2×C43C2×#45311yescharacteristic
320C2×C43#301811yescharacteristic
321D43—44no—
322D43—82no—
323C2×H(5,𝔽2)—431no—
324C2×AGL(1,ℤ/8)—432no—
325C2×#127—431no—
326#520—432no—
327#520—862no—
328#518—431no—
329#518—862no—
330#518—862no—
331C4×#41—432no—
332C4×#41—862no—
333C2×C4×D4—431no—
334C2×C4×D4—862no—
335C2×C4×D4—862no—
336C2×C4×D4—862no—
337C2×C4×D4C2×D4311yescharacteristic
338#453—438no—
339#442—862no—
340#440—862no—
341C4×SD16—862no—
342C4×D8—862no—
343#428—432no—
344C2×#104—432no—
345C2×#104—432no—
346#418—432no—
347#417—432no—
348C2×#100C2×D4311yescharacteristic
349C2×#100C2×D4311yescharacteristic
350C4×M16C2×D4312yescomplemented
351#390—431no—
352#390—431no—
353#390—862no—
354#384—431no—
355C43—431no—
356#343C2×D4312yescomplemented
357#339—432no—
358#339—432no—
359C43C4×#45311yescharacteristic, complemented, Sylow
360H(5,𝔽2)—434no—
361H(5,𝔽2)—864no—
362H(5,𝔽2)—862no—
363C2×#41—432no—
364C2×#41—862no—
365C22×D4—431no—
366C22×D4—862no—
367C22×D4—862no—
368C22×D4—862no—
369C22×D4C22×D4311yescharacteristic
370C23×C4—862no—
371C23×C4—861no—
372C23×C4D17212yes—
373AGL(1,ℤ/8)—438no—
374AGL(1,ℤ/8)—864no—
375C2×SD16—862no—
376C2×D8—862no—
377C2×M16C22×D4312yes—
378C2×M16C22×D4312yes—
379#127—434no—
380#127—862no—
381C4×Q8—432no—
382C4×Q8—432no—
383C4×Q8—862no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—432no—
387C4×D4—432no—
388C4×D4—864no—
389C4×D4—864no—
390C4×D4—862no—
391C4×D4—862no—
392C4×D4—862no—
393C4×D4—864no—
394C4×D4—864no—
395C4×D4—862no—
396C4×D4—864no—
397C4×D4—862no—
398C4×D4—862no—
399C4×D4—862no—
400C4×D4—1728no—
401#117—432no—
402#117—864no—
403#117—862no—
404#117—862no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—862no—
407C2×C4⋊C4—862no—
408C2×C4⋊C4—862no—
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C22⋊C4—864no—
411C2×C22⋊C4—862no—
412C2×C22⋊C4—862no—
413C2×C22⋊C4—862no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—862no—
416C2×C22⋊C4D17212yes—
417C2×C42—431no—
418C2×C42—431no—
419C2×C42—862no—
420C2×C42—861no—
421C2×C42—862no—
422C2×C42—861no—
423C2×C42C22×D4311yescharacteristic
424#107—862no—
425#106—862no—
426#104—438no—
427#104—864no—
428#103—862no—
429#102—862no—
430#102—862no—
431#102—862no—
432#100—22no—
433#100C4×D4314yescomplemented
434#97—22no—
435C4×C8—22no—
436C24—862no—
437C24—861no—
438C24C2×D17212yes—
439#41—434no—
440#41—434no—
441#41—868no—
442#41—868no—
443#41—862no—
444#41—862no—
445C2×Q8—432no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—432no—
449C2×D4—432no—
450C2×D4—868no—
451C2×D4—868no—
452C2×D4—864no—
453C2×D4—868no—
454C2×D4—868no—
455C2×D4—862no—
456C2×D4—868no—
457C2×D4—862no—
458C2×D4—862no—
459C2×D4—861no—
460C2×D4—1724no—
461C2×D4—1724no—
462C2×D4C2×C4×D4312yes—
463C2×D4#1062189812yes—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—44no—
467C22×C4—864no—
468C22×C4—862no—
469C22×C4—861no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—861no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—861no—
477C22×C4—3444no—
478C22×C4—1724no—
479C22×C4—1721no—
480C22×C4—1721no—
481C22×C4C2×D17211yescharacteristic
482C22×C4C2×D17212yes—
483C22×C4C2×D17211yescharacteristic
484C22×C4C23×D4311yescharacteristic
485SD16—868no—
486D8—868no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16C2×C4×D4314yescomplemented
491C2×C8—22no—
492C2×C8—22no—
493C4⋊C4—22no—
494C4⋊C4—432no—
495C4⋊C4—432no—
496C4⋊C4—864no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—1724no—
501C22⋊C4—24no—
502C22⋊C4—864no—
503C22⋊C4—864no—
504C22⋊C4—862no—
505C22⋊C4—862no—
506C22⋊C4—862no—
507C22⋊C4—1724no—
508C22⋊C4—1724no—
509C22⋊C4—1722no—
510C42—432no—
511C42—864no—
512C42—864no—
513C42—862no—
514C42—862no—
515C42—862no—
516C42—861no—
517C42—862no—
518C42—1722no—
519C42D4×D4312yes—
520C42D4×D4312yes—
521C23—22no—
522C23—22no—
523C23—42no—
524C23—42no—
525C23—868no—
526C23—862no—
527C23—862no—
528C23—3442no—
529C23—3442no—
530C23—1722no—
531C23—1722no—
532C23—1721no—
533C23—1721no—
534C23C4×D17214yes—
535C23C22×D17211yescharacteristic
536Q8—434no—
537Q8—862no—
538D4—24no—
539D4—24no—
540D4—434no—
541D4—8616no—
542D4—864no—
543D4—864no—
544D4—864no—
545D4—862no—
546D4—17216no—
547D4—1722no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—44no—
552C2×C4—42no—
553C2×C4—82no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—868no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—864no—
560C2×C4—864no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—3442no—
565C2×C4—3442no—
566C2×C4—3444no—
567C2×C4—3442no—
568C2×C4—3442no—
569C2×C4—3442no—
570C2×C4—1722no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1724no—
575C2×C4#1306329512yes—
576C2×C4#1306329511yescharacteristic
577C2×C4#1306329511yescharacteristic
578C2×C4C22×C4×D4311yescharacteristic
579C2×C4C2×D4×D4312yes—
580C2×C4#41×D4312yes—
581C2×C4C2×#1062189811yescharacteristic
582C8—24no—
583C8—42no—
584C22—21no—
585C22—21no—
586C22—24no—
587C22—44no—
588C22—42no—
589C22—42no—
590C22—82no—
591C22—864no—
592C22—3442no—
593C22—3448no—
594C22—3441no—
595C22—3441no—
596C22—1724no—
597C22—1722no—
598C22—1722no—
599C22—1722no—
600C22C2×C4×D17211yescharacteristic
601C22C2×#1306329511yescharacteristic
602C22#1458341111yescharacteristic
603C4—22no—
604C4—21no—
605C4—42no—
606C4—864no—
607C4—864no—
608C4—3441no—
609C4—1722no—
610C4—1722no—
611C4—1722no—
612C4#1458306912yesdirect product factor
613C4C4×D4×D4312yes—
614C4#1458340812yes—
615C2—21no—
616C2—21no—
617C2—44no—
618C2—3442no—
619C2—1724no—
620C2C4×#1306329511yescharacteristic
621C2C2×#1458306911yescharacteristic
622C2#1914394811yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#100×C43C2
socleC22×C43C2×#120
prime radicalC2×#14583069C2
cosocleC22×C4×C43C24
hypercenterC4×#100D43
hypocenterC43C4×#453
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#100

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C4×#13063370C2semidirect
3. C4×#13063353C2semidirect
4. C4×#13063321C2semidirect
5. #19134991C2semidirect
6. #19134970C2semidirect
7. #19134824C2semidirect
8. #19134807C2semidirect
9. #19134551C2semidirect
10. C4×#13063251C2semidirect
11. C4×#100×C43C2semidirect
22. C2×C4×D172C22semidirect
26. #14583069C4direct (N × H)
31. #14582941C22semidirect
34. #14582905C22semidirect
37. #14582800C22semidirect
39. #14582768C22semidirect
40. C42×Dic43C22semidirect
41. #14582660C22semidirect
42. #14582660C22semidirect
46. C4×M16×C43C22semidirect
47. C43×#343C22semidirect
50. #13063370C2×C4semidirect
60. #13063353C2×C4semidirect
64. #13063321C2×C4semidirect
65. C4×Dic86D4semidirect
66. C4×Dic86D4semidirect
70. C4×D172D4semidirect
71. C4×D172D4semidirect
106. #13063251C2×C4semidirect
121. #100×C43C2×C4semidirect
162. C2×D172C22×C4semidirect
176. M16×C43C22×C4semidirect
206. C4×Dic43C22×C4semidirect
260. D172C4×D4semidirect
269. Dic86C4×D4semidirect
295. C4×C43#453semidirect
314. C4×#100D43semidirect
350. C4×M16C2×D43semidirect
356. #343C2×D43semidirect
359. C43C4×#453semidirect
433. #100C4×D43semidirect
490. M16C2×C4×D43semidirect
612. C4#14583069direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×#130633702
C2×#145830692
C4×#130633532
C4×#130633212
#191349912
#191349702
#191348242
#191348072
#191345512
C4×#130632512
C4×#100×C432
C4×#45343